Bulletin of the Korean Mathematical Society (대한수학회보)

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UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON ℝN

  • Received : 2012.04.04
  • Published : 2014.09.30
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Abstract

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

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Acknowledgement

Supported by : Vietnam Ministry of Education and Training

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